Results 21 to 30 of about 7,729 (158)
Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications
, 2015 In this paper we extend Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds for dimension $n\ne 2$. As one application, we solve a generalized Yamabe problem on locally conforamlly flat manifolds via a new designed energy functional and
Han, Yazhou, Zhu, Meijun
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Singular solutions of fractional order conformal Laplacians
, 2011 We investigate the singular sets of solutions of conformally covariant elliptic operators of fractional order with the goal of developing generalizations of some well-known properties of solutions of the singular Yamabe ...
Gonzalez, Maria del Mar +2 more
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Generic Properties of Critical Points of the Weyl Tensor
Advanced Nonlinear Studies, 2017 Given (M,g)${(M,g)}$, a smooth compact Riemannian n-manifold, we prove that for a generic Riemannian metric g the critical points of the function š²gā¢(Ī¾):=|Weylgā¢(Ī¾)|g2${\mathcal{W}_{g}(\xi):=\lvert\mathrm{Weyl}_{g}(\xi)\rvert^{2}_{g}}$ with š²gā¢(Ī¾)ā 0 ...
Micheletti Anna Maria, Pistoia Angela
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The Yamabe problem on Dirichlet spaces [PDF]
, 2013 We continue our previous work studying critical exponent semilinear elliptic (and subelliptic) problems which generalize the classical Yamabe problem. In [3] the focus was on metric-measure spaces with an `almost smooth' structure, with stratified spaces
Gilles Carron +3 more
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Fractional Q$Q$ācurvature on the sphere and optimal partitions
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional Q$Q$ācurvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of a symmetric minimal partition through a variational approach. A key ingredient in our analysis is a new
HĆ©ctor A. ChangāLara +2 more
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Kodaira Dimension and the Yamabe Problem [PDF]
, 1997 The Yamabe invariant Y(M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unit-volume constant-scalar curvature Riemannian metrics g on M.
LeBrun, Claude
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Invariant surface area functionals and singular Yamabe problem in 3-dimensional CR geometry
, 2017 We express two CR invariant surface area elements in terms of quantities in pseudohermitian geometry. We deduce the Euler-Lagrange equations of the associated energy functionals. Many solutions are given and discussed.
Cheng, Jih-Hsin +2 more
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Abstract and Applied Analysis, 2014 We present a numerical method for a class of boundary value problems on the unit interval which feature a type of power-law nonlinearity. In order to numerically solve this type of nonlinear boundary value problems, we construct a kind of spectral ...
A. H. Bhrawy +2 more
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On Yamabe type problems on Riemannian manifolds with boundary
, 2015 Let $(M,g)$ be a $n-$dimensional compact Riemannian manifold with boundary. We consider the Yamabe type problem \begin{equation} \left\{ \begin{array}{ll} -\Delta_{g}u+au=0 & \text{ on }M \\ \partial_\nu u+\frac{n-2}{2}bu= u^{{n\over n-2}\pm\varepsilon} &
Ghimenti, Marco +2 more
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Conformal metrics of constant scalar curvature with unbounded volumes
Proceedings of the London Mathematical Society, Volume 131, Issue 1, July 2025.Abstract For nā©¾25$n\geqslant 25$, we construct a smooth metric gā¼$\tilde{g}$ on the standard n$n$ādimensional sphere Sn$\mathbb {S}^n$ such that there exists a sequence of smooth metrics {gā¼k}kāN$\lbrace \tilde{g}_k\rbrace _{k\in \mathbb {N}}$ conformal to gā¼$\tilde{g}$ where each gā¼k$\tilde{g}_k$ has scalar curvature Rgā¼kā”1$R_{\tilde{g}_k}\equiv 1 ...
Liuwei Gong, Yanyan Li
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